proposition 3.57 Composition of bijective maps
open in the book ·
parts/02-mathematical-methods/01-logic-sets.tex:1428
· p. 33
Rests on
-
depends_on
definition 3.51
Inverse map
¶
- depends_on definition 3.47 Bijective map ¶
- depends_on definition 3.49 Composition map ¶
- depends_on definition 3.50 Identity map ¶
-
depends_on
proposition 3.56
Composition is associative
¶
- depends_on definition 3.49 Composition map ¶ ↺
- depends_on definition 3.50 Identity map ¶ ↺
- proves proof ch:01-logic-sets@proof-9 ¶
-
depends_on
proposition 3.48
Characterization of bijectivity
¶
- depends_on definition 3.47 Bijective map ¶ ↺
- depends_on definition 3.45 Injective map ¶
- depends_on definition 3.46 Surjective map ¶
- proves proof ch:01-logic-sets@proof-7 ¶
- proves proof ch:01-logic-sets@proof-10 ¶
Supports
- depends_on proposition 3.63 prop:inf-equipotence-equivalence ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Inverse map | declared | parts/02-mathematical-methods/01-logic-sets.tex:1435 |
depends_on |
→ | Composition is associative | declared | parts/02-mathematical-methods/01-logic-sets.tex:1435 |
depends_on |
→ | Characterization of bijectivity | declared | parts/02-mathematical-methods/01-logic-sets.tex:1435 |
depends_on |
← | prop:inf-equipotence-equivalence | declared | parts/02-mathematical-methods/01-logic-sets.tex:1637 |
proves |
← | ch:01-logic-sets@proof-10 | declared | parts/02-mathematical-methods/01-logic-sets.tex:1438 |